A particle of mass $m$ makes a head-on elastic collision with a particle of mass $2m$initially at rest. The velocity of the first particle before and after the collision is $u_1$and $v_1$ . Assume that no external force is acting. Then which of the following statement(s) is/are true for this collision? 

Linear momentum conservation $m{u}_1 = 2m{v}_2+m{v}_1$

Newton’s law of collision $-1 = \frac{v_2-v_1}{0 - u_1} \Rightarrow v_1 = \frac{-u_1}{3}$

$u_2-u_1 \Rightarrow \frac{{\displaystyle \frac{1}{2}}m{v_1}^2-{\displaystyle \frac{1}{2}}m{u_1}^2}{\frac{1}{2}m{u_1}^2}\Rightarrow \frac{{\displaystyle \frac{1}{9}}-1}{1} \Rightarrow -\frac{8}{9}\Rightarrow loss$

loss of $KE$ of first particle $=$ gain in $KE$of second in elastic collision

During the course of collision , external force acting on the system is zero, hence momentum of the system is constant .